The Random Walker Printer

Matlab, 112

The core idea is generating a list of possible next positions and then uniformly drawing one of them. If we are e.g. at position $l=1$ the possible steps would be [-1,0,1,2,3] Of course if we would chose -1 that would be invalid and we would have to stay at the same position. Thats why we replace the invalid positions with the current position, [1,0,1,2,3], and then randomly chose an element from this updated list.

The OP asked us tho draw the program, so here we go:

The transcription:

function c(n,s);
l=19;                             %initialize position
for k=1:n;                          
    disp([ones(1,l)*32,'.']);     %print the line
    z=(-2:2)+l;                   %get vector of possible next steps (for l=1 we get [-1,0,1,2,3])
    z(z<0)=l;                     %prune invalids: here we just replace the the invalid positions with the current position
    z(z>39)=l;                    %   this ensures the same behaivour as staying in the same spot when going outside of the range
    l=z(randi(5));                %draw random sample of those
    pause(s);
end

Perl, 136 128 116 106 101 90 86

$p=19;map{say$"x$p.".";sleep $ARGV[0];$x=rand(5)+$p-2;$p=$x>0&&$x<40?$x:$p}1..$ARGV[1]

Requires the seconds to be an integer.

Run with perl <filename> <second delay> <number of steps>.

There may be more golfing potential here, although honestly, I'm surprised it got this far. (Come on, only 6 more bytes to beat the bash answer...)

Changes

• Saved 8 bytes by removing unneeded parentheses and spelling out ARGV (it's actually shorter that way)
• Saved 12 more bytes by removing $s and $n and just using the plain $ARGV[0] and $ARGV[1]
• Saved another 10 bytes when I realized I could use $" and didn't need to specifically define $u as $undef.
• Saved 5 more bytes by rearranging the ternary and how $x is used and by using map instead of for.
• Saved 11 bytes by no longer accepting the seconds as decimals (challenge spec says it's OK.)
• Saved another 5 bytes by using say instead of print.

Pyth, 39

J19VEK+.d0QW<.d0K)+*d=JhtS[Z39-+O5J2)\.

Takes s as the first line of input and n as the second. Works on the command line but not with the online interpreter. My first Pyth program ever! Golfing tips are appreciated.